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A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [14]
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, p-adic, and/or algebraic points under repeated application of a polynomial or rational function.
In the logistic map, r is a parameter, and x is a variable. It is a map in the sense that it maps a configuration or phase space to itself (in this simple case the space is one dimensional in the variable x), it can be interpreted as a tool to get next position in the configuration space after one time step.
In control engineering, a discrete-event dynamic system (DEDS) is a discrete-state, event-driven system of which the state evolution depends entirely on the occurrence of asynchronous discrete events over time.
The Kuramoto–Sivashinsky equation is an example of a spatiotemporally continuous dynamical system that exhibits period doubling. It is one of the most well-studied nonlinear partial differential equations , originally introduced as a model of flame front propagation.
A discrete-event simulation (DES) models the operation of a system as a sequence of events in time. Each event occurs at a particular instant in time and marks a change of state in the system. [ 1 ] Between consecutive events, no change in the system is assumed to occur; thus the simulation time can directly jump to the occurrence time of the ...
A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior – a system that can both flow (described by a differential equation) and jump (described by a state machine, automaton, or a difference equation). [1]